Herzog, Gerd; Schmoeger, Christoph A note on a theorem of Raubenheimer and Rode. (English) Zbl 1055.46032 Proc. Am. Math. Soc. 131, No. 11, 3507-3509 (2003). H. Raubenheimer and S. Rode [Indag. Math., New Ser. 7, No. 4, 489–502 (1996; Zbl 0887.46026)] proved that if \(A\) is a unital complex Banach algebra which is ordered by an algebra wedge \(W\) and the spectral radius is increasing on \(W\), then \(r(a)\in \sigma(a)\). Here the authors obtain a converse result, namely, \(r(a)\in\sigma(a)\) implies the existence of a suitable wedge \(W\). Reviewer: Wiesław Tadeusz Żelazko (Warszawa) Cited in 3 Documents MSC: 46H05 General theory of topological algebras Keywords:algebra wedge; spectrum; spectral radius Citations:Zbl 0887.46026 PDFBibTeX XMLCite \textit{G. Herzog} and \textit{C. Schmoeger}, Proc. Am. Math. Soc. 131, No. 11, 3507--3509 (2003; Zbl 1055.46032) Full Text: DOI References: [1] Sterling K. Berberian, Lectures in functional analysis and operator theory, Springer-Verlag, New York-Heidelberg, 1974. Graduate Texts in Mathematics, No. 15. · Zbl 0296.46002 [2] H. Raubenheimer and S. Rode, Cones in Banach algebras, Indag. Math. (N.S.) 7 (1996), no. 4, 489 – 502. · Zbl 0887.46026 · doi:10.1016/S0019-3577(97)89135-5 [3] Walter Rudin, Functional analysis, 2nd ed., International Series in Pure and Applied Mathematics, McGraw-Hill, Inc., New York, 1991. · Zbl 0867.46001 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.